src/Pure/Isar/proof.ML
author wenzelm
Wed Dec 19 00:28:27 2001 +0100 (2001-12-19)
changeset 12549 65f03a3f7998
parent 12534 5729b8cac4e1
child 12698 b87b41ade3b2
permissions -rw-r--r--
tuned interface of ProofContext.generalize;
tuned;
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(*  Title:      Pure/Isar/proof.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Proof states and methods.
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*)
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signature BASIC_PROOF =
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sig
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  val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
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  val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
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end;
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signature PROOF =
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sig
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  include BASIC_PROOF
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  type context
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  type state
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  exception STATE of string * state
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  val check_result: string -> state -> 'a Seq.seq -> 'a Seq.seq
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  val init_state: theory -> state
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  val context_of: state -> context
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  val theory_of: state -> theory
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  val sign_of: state -> Sign.sg
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  val warn_extra_tfrees: state -> state -> state
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  val reset_thms: string -> state -> state
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  val the_facts: state -> thm list
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  val the_fact: state -> thm
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  val get_goal: state -> context * (thm list * thm)
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  val goal_facts: (state -> thm list) -> state -> state
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  val use_facts: state -> state
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  val reset_facts: state -> state
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  val is_chain: state -> bool
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  val assert_forward: state -> state
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  val assert_forward_or_chain: state -> state
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  val assert_backward: state -> state
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  val assert_no_chain: state -> state
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  val enter_forward: state -> state
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  val verbose: bool ref
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  val pretty_state: int -> state -> Pretty.T list
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  val pretty_goals: bool -> state -> Pretty.T list
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  val level: state -> int
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  type method
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  val method: (thm list -> tactic) -> method
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  val method_cases: (thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> method
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  val refine: (context -> method) -> state -> state Seq.seq
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  val refine_end: (context -> method) -> state -> state Seq.seq
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  val match_bind: (string list * string) list -> state -> state
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  val match_bind_i: (term list * term) list -> state -> state
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  val let_bind: (string list * string) list -> state -> state
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  val let_bind_i: (term list * term) list -> state -> state
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  val simple_have_thms: string -> thm list -> state -> state
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  val have_thmss: ((string * context attribute list) *
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    (thm list * context attribute list) list) list -> state -> state
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  val with_thmss: ((string * context attribute list) *
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    (thm list * context attribute list) list) list -> state -> state
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  val fix: (string list * string option) list -> state -> state
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  val fix_i: (string list * typ option) list -> state -> state
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  val assm: ProofContext.exporter
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val assm_i: ProofContext.exporter
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val assume:
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    ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val assume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val presume:
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    ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val presume_i: ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val def: string -> context attribute list -> string *  (string * string list) -> state -> state
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  val def_i: string -> context attribute list -> string * (term * term list) -> state -> state
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  val invoke_case: string * string option list * context attribute list -> state -> state
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  val multi_theorem: string -> bstring * theory attribute list
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    -> (xstring * context attribute list) option -> context attribute Locale.element list
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    -> ((bstring * theory attribute list) * (string * (string list * string list)) list) list
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    -> theory -> state
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  val multi_theorem_i: string -> bstring * theory attribute list
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    -> (string * context attribute list) option -> context attribute Locale.element_i list
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    -> ((bstring * theory attribute list) * (term * (term list * term list)) list) list
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    -> theory -> state
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  val theorem: string
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    -> (xstring * context attribute list) option -> context attribute Locale.element list
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    -> bstring -> theory attribute list -> string * (string list * string list) -> theory -> state
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  val theorem_i: string
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    -> (string * context attribute list) option -> context attribute Locale.element_i list
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    -> bstring -> theory attribute list -> term * (term list * term list) -> theory -> state
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  val chain: state -> state
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  val from_facts: thm list -> state -> state
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  val show: (bool -> state -> state) -> (state -> state Seq.seq)
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> bool -> state -> state
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  val show_i: (bool -> state -> state) -> (state -> state Seq.seq)
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> bool -> state -> state
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  val have: (state -> state Seq.seq)
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    -> ((string * context attribute list) * (string * (string list * string list)) list) list
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    -> state -> state
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  val have_i: (state -> state Seq.seq)
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    -> ((string * context attribute list) * (term * (term list * term list)) list) list
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    -> state -> state
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  val at_bottom: state -> bool
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  val local_qed: (state -> state Seq.seq)
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    -> (context -> string * (string * thm list) list -> unit) * (context -> thm -> unit)
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    -> state -> state Seq.seq
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  val global_qed: (state -> state Seq.seq) -> state
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    -> (theory * ((string * string) * (string * thm list) list)) Seq.seq
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  val begin_block: state -> state
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  val end_block: state -> state Seq.seq
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  val next_block: state -> state
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end;
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signature PRIVATE_PROOF =
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sig
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  include PROOF
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  val put_data: Object.kind -> ('a -> Object.T) -> 'a -> state -> state
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end;
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structure Proof: PRIVATE_PROOF =
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struct
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(** proof state **)
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type context = ProofContext.context;
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(* type goal *)
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datatype kind =
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  Theorem of string *                           (*theorem kind*)
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    (bstring * theory attribute list) *         (*common result binding*)
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    (string * context attribute list) option *  (*target locale*)
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    theory attribute list list |                (*attributes of individual result binding*)
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  Show of context attribute list list |         (*intermediate result, solving subgoal*)
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  Have of context attribute list list;          (*intermediate result*)
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fun common_name "" = "" | common_name a = " " ^ a;
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fun kind_name _ (Theorem (s, (a, _), None, _)) = s ^ common_name a
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  | kind_name sg (Theorem (s, (a, _), Some (name, _), _)) =
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      s ^ common_name a ^ " (in " ^ Locale.cond_extern sg name ^ ")"
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  | kind_name _ (Show _) = "show"
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  | kind_name _ (Have _) = "have";
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type goal =
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 (kind *             (*result kind*)
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  string list *      (*result names*)
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  term list list) *  (*result statements*)
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 (thm list *         (*use facts*)
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  thm);              (*goal: subgoals ==> statement*)
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(* type mode *)
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datatype mode = Forward | ForwardChain | Backward;
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val mode_name = (fn Forward => "state" | ForwardChain => "chain" | Backward => "prove");
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(* datatype state *)
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datatype node =
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  Node of
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   {context: context,
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    facts: thm list option,
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    mode: mode,
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    goal: (goal * (state -> state Seq.seq)) option}
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and state =
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  State of
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    node *              (*current*)
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    node list;          (*parents wrt. block structure*)
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fun make_node (context, facts, mode, goal) =
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  Node {context = context, facts = facts, mode = mode, goal = goal};
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exception STATE of string * state;
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fun err_malformed name state =
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  raise STATE (name ^ ": internal error -- malformed proof state", state);
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fun check_result msg state sq =
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  (case Seq.pull sq of
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    None => raise STATE (msg, state)
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  | Some s_sq => Seq.cons s_sq);
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fun map_current f (State (Node {context, facts, mode, goal}, nodes)) =
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  State (make_node (f (context, facts, mode, goal)), nodes);
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fun init_state thy =
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  State (make_node (ProofContext.init thy, None, Forward, None), []);
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(** basic proof state operations **)
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(* context *)
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fun context_of (State (Node {context, ...}, _)) = context;
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val theory_of = ProofContext.theory_of o context_of;
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val sign_of = ProofContext.sign_of o context_of;
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fun map_context f = map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
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fun map_context_result f (state as State (Node {context, facts, mode, goal}, nodes)) =
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  let val (context', result) = f context
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  in (State (make_node (context', facts, mode, goal), nodes), result) end;
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fun put_data kind f = map_context o ProofContext.put_data kind f;
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val warn_extra_tfrees = map_context o ProofContext.warn_extra_tfrees o context_of;
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val add_binds_i = map_context o ProofContext.add_binds_i;
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val auto_bind_goal = map_context o ProofContext.auto_bind_goal;
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val auto_bind_facts = map_context o ProofContext.auto_bind_facts;
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val put_thms = map_context o ProofContext.put_thms;
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val put_thmss = map_context o ProofContext.put_thmss;
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val reset_thms = map_context o ProofContext.reset_thms;
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val get_case = ProofContext.get_case o context_of;
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(* facts *)
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fun the_facts (State (Node {facts = Some facts, ...}, _)) = facts
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  | the_facts state = raise STATE ("No current facts available", state);
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fun the_fact state =
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  (case the_facts state of
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    [thm] => thm
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  | _ => raise STATE ("Single fact expected", state));
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fun assert_facts state = (the_facts state; state);
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fun get_facts (State (Node {facts, ...}, _)) = facts;
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val thisN = "this";
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fun put_facts facts state =
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  state
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  |> map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal))
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  |> (case facts of None => reset_thms thisN | Some ths => put_thms (thisN, ths));
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val reset_facts = put_facts None;
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fun these_factss (state, named_factss) =
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  state
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  |> put_thmss named_factss
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  |> put_facts (Some (flat (map #2 named_factss)));
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(* goal *)
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local
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  fun find i (state as State (Node {goal = Some goal, ...}, _)) = (context_of state, (i, goal))
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    | find i (State (Node {goal = None, ...}, node :: nodes)) = find (i + 1) (State (node, nodes))
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    | find _ (state as State (_, [])) = err_malformed "find_goal" state;
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in val find_goal = find 0 end;
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fun get_goal state =
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  let val (ctxt, (_, ((_, x), _))) = find_goal state
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  in (ctxt, x) end;
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fun put_goal goal = map_current (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
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fun map_goal f g (State (Node {context, facts, mode, goal = Some goal}, nodes)) =
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      State (make_node (f context, facts, mode, Some (g goal)), nodes)
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  | map_goal f g (State (nd, node :: nodes)) =
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      let val State (node', nodes') = map_goal f g (State (node, nodes))
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      in map_context f (State (nd, node' :: nodes')) end
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  | map_goal _ _ state = state;
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fun goal_facts get state =
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  state
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  |> map_goal I (fn ((result, (_, thm)), f) => ((result, (get state, thm)), f));
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fun use_facts state =
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  state
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  |> goal_facts the_facts
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  |> reset_facts;
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(* mode *)
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fun get_mode (State (Node {mode, ...}, _)) = mode;
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fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
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val enter_forward = put_mode Forward;
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val enter_forward_chain = put_mode ForwardChain;
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val enter_backward = put_mode Backward;
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fun assert_mode pred state =
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  let val mode = get_mode state in
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    if pred mode then state
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    else raise STATE ("Illegal application of proof command in "
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      ^ quote (mode_name mode) ^ " mode", state)
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  end;
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fun is_chain state = get_mode state = ForwardChain;
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val assert_forward = assert_mode (equal Forward);
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val assert_forward_or_chain = assert_mode (equal Forward orf equal ForwardChain);
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val assert_backward = assert_mode (equal Backward);
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val assert_no_chain = assert_mode (not_equal ForwardChain);
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(* blocks *)
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fun level (State (_, nodes)) = length nodes;
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fun open_block (State (node, nodes)) = State (node, node :: nodes);
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fun new_block state =
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  state
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  |> open_block
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  |> put_goal None;
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fun close_block (state as State (_, node :: nodes)) = State (node, nodes)
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  | close_block state = raise STATE ("Unbalanced block parentheses", state);
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(** pretty_state **)
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val verbose = ProofContext.verbose;
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fun pretty_goals_local ctxt = Display.pretty_goals_aux
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  (ProofContext.pretty_sort ctxt, ProofContext.pretty_typ ctxt, ProofContext.pretty_term ctxt);
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fun pretty_facts _ _ None = []
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  | pretty_facts s ctxt (Some ths) =
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      [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
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fun pretty_state nr (state as State (Node {context = ctxt, facts, mode, goal = _}, nodes)) =
wenzelm@5820
   338
  let
wenzelm@11891
   339
    val ref (_, _, begin_goal) = Display.current_goals_markers;
wenzelm@5820
   340
wenzelm@5820
   341
    fun levels_up 0 = ""
wenzelm@7575
   342
      | levels_up 1 = ", 1 level up"
wenzelm@7575
   343
      | levels_up i = ", " ^ string_of_int i ^ " levels up";
wenzelm@5820
   344
wenzelm@11556
   345
    fun subgoals 0 = ""
wenzelm@11556
   346
      | subgoals 1 = ", 1 subgoal"
wenzelm@11556
   347
      | subgoals n = ", " ^ string_of_int n ^ " subgoals";
wenzelm@12146
   348
wenzelm@12146
   349
    fun prt_names names =
wenzelm@12242
   350
      (case filter_out (equal "") names of [] => ""
wenzelm@12308
   351
      | nms => " " ^ enclose "(" ")" (space_implode " and " (take (7, nms) @
wenzelm@12308
   352
          (if length nms > 7 then ["..."] else []))));
wenzelm@12146
   353
wenzelm@12146
   354
    fun prt_goal (_, (i, (((kind, names, _), (goal_facts, thm)), _))) =
wenzelm@12085
   355
      pretty_facts "using " ctxt
wenzelm@8462
   356
        (if mode <> Backward orelse null goal_facts then None else Some goal_facts) @
wenzelm@12146
   357
      [Pretty.str ("goal (" ^ kind_name (sign_of state) kind ^ prt_names names ^
wenzelm@12146
   358
          levels_up (i div 2) ^ subgoals (Thm.nprems_of thm) ^ "):")] @
wenzelm@12085
   359
      pretty_goals_local ctxt begin_goal (true, true) (! Display.goals_limit) thm;
wenzelm@6848
   360
wenzelm@8462
   361
    val ctxt_prts =
wenzelm@12085
   362
      if ! verbose orelse mode = Forward then ProofContext.pretty_context ctxt
wenzelm@12085
   363
      else if mode = Backward then ProofContext.pretty_asms ctxt
wenzelm@7575
   364
      else [];
wenzelm@8462
   365
wenzelm@8462
   366
    val prts =
wenzelm@8582
   367
     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
wenzelm@12010
   368
        (if ! verbose then ", depth " ^ string_of_int (length nodes div 2 - 1)
wenzelm@8561
   369
        else "")), Pretty.str ""] @
wenzelm@8462
   370
     (if null ctxt_prts then [] else ctxt_prts @ [Pretty.str ""]) @
wenzelm@8462
   371
     (if ! verbose orelse mode = Forward then
wenzelm@12146
   372
       (pretty_facts "" ctxt facts @ prt_goal (find_goal state))
wenzelm@12085
   373
      else if mode = ForwardChain then pretty_facts "picking " ctxt facts
wenzelm@12146
   374
      else prt_goal (find_goal state))
wenzelm@12423
   375
  in prts end;
wenzelm@5820
   376
wenzelm@12085
   377
fun pretty_goals main state =
wenzelm@12085
   378
  let val (ctxt, (_, ((_, (_, thm)), _))) = find_goal state
wenzelm@12085
   379
  in pretty_goals_local ctxt "" (false, main) (! Display.goals_limit) thm end;
wenzelm@10320
   380
wenzelm@5820
   381
wenzelm@5820
   382
wenzelm@5820
   383
(** proof steps **)
wenzelm@5820
   384
wenzelm@5820
   385
(* datatype method *)
wenzelm@5820
   386
wenzelm@8374
   387
datatype method =
wenzelm@8374
   388
  Method of thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq;
wenzelm@8374
   389
wenzelm@8374
   390
fun method tac = Method (fn facts => fn st => Seq.map (rpair []) (tac facts st));
wenzelm@8374
   391
val method_cases = Method;
wenzelm@5820
   392
wenzelm@5820
   393
wenzelm@5820
   394
(* refine goal *)
wenzelm@5820
   395
wenzelm@8234
   396
local
wenzelm@8234
   397
wenzelm@5820
   398
fun check_sign sg state =
wenzelm@5820
   399
  if Sign.subsig (sg, sign_of state) then state
wenzelm@5820
   400
  else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);
wenzelm@5820
   401
wenzelm@8234
   402
fun gen_refine current_context meth_fun state =
wenzelm@6848
   403
  let
wenzelm@10553
   404
    val (goal_ctxt, (_, ((result, (facts, thm)), f))) = find_goal state;
wenzelm@8234
   405
    val Method meth = meth_fun (if current_context then context_of state else goal_ctxt);
wenzelm@5820
   406
wenzelm@8374
   407
    fun refn (thm', cases) =
wenzelm@6848
   408
      state
wenzelm@6848
   409
      |> check_sign (Thm.sign_of_thm thm')
wenzelm@8374
   410
      |> map_goal (ProofContext.add_cases cases) (K ((result, (facts, thm')), f));
wenzelm@6848
   411
  in Seq.map refn (meth facts thm) end;
wenzelm@5820
   412
wenzelm@8234
   413
in
wenzelm@8234
   414
wenzelm@8234
   415
val refine = gen_refine true;
wenzelm@8234
   416
val refine_end = gen_refine false;
wenzelm@8234
   417
wenzelm@8234
   418
end;
wenzelm@8234
   419
wenzelm@5820
   420
wenzelm@11917
   421
(* goal addressing *)
wenzelm@6932
   422
wenzelm@8152
   423
fun FINDGOAL tac st =
wenzelm@8374
   424
  let fun find (i, n) = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1, n))
wenzelm@8374
   425
  in find (1, Thm.nprems_of st) st end;
wenzelm@8152
   426
wenzelm@8166
   427
fun HEADGOAL tac = tac 1;
wenzelm@8166
   428
wenzelm@9469
   429
wenzelm@9469
   430
(* export results *)
wenzelm@9469
   431
wenzelm@11816
   432
fun refine_tac rule =
wenzelm@11816
   433
  Tactic.rtac rule THEN_ALL_NEW (SUBGOAL (fn (goal, i) =>
wenzelm@11816
   434
    if can Logic.dest_goal (Logic.strip_assums_concl goal) then
wenzelm@11816
   435
      Tactic.etac Drule.triv_goal i
wenzelm@11816
   436
    else all_tac));
wenzelm@11816
   437
wenzelm@12146
   438
fun export_goal inner print_rule raw_rule state =
wenzelm@6932
   439
  let
wenzelm@10553
   440
    val (outer, (_, ((result, (facts, thm)), f))) = find_goal state;
wenzelm@12010
   441
    val exp_tac = ProofContext.export true inner outer;
wenzelm@9469
   442
    fun exp_rule rule =
wenzelm@9469
   443
      let
wenzelm@12055
   444
        val _ = print_rule outer rule;
wenzelm@11816
   445
        val thmq = FINDGOAL (refine_tac rule) thm;
wenzelm@9469
   446
      in Seq.map (fn th => map_goal I (K ((result, (facts, th)), f)) state) thmq end;
wenzelm@9469
   447
  in raw_rule |> exp_tac |> (Seq.flat o Seq.map exp_rule) end;
wenzelm@6932
   448
wenzelm@12146
   449
fun export_goals inner print_rule raw_rules =
wenzelm@12146
   450
  Seq.EVERY (map (export_goal inner print_rule) raw_rules);
wenzelm@12146
   451
wenzelm@6932
   452
fun transfer_facts inner_state state =
wenzelm@6932
   453
  (case get_facts inner_state of
wenzelm@6932
   454
    None => Seq.single (reset_facts state)
wenzelm@8617
   455
  | Some thms =>
wenzelm@8617
   456
      let
wenzelm@12010
   457
        val exp_tac = ProofContext.export false (context_of inner_state) (context_of state);
wenzelm@11816
   458
        val thmqs = map exp_tac thms;
wenzelm@8617
   459
      in Seq.map (fn ths => put_facts (Some ths) state) (Seq.commute thmqs) end);
wenzelm@6932
   460
wenzelm@6932
   461
wenzelm@6932
   462
(* prepare result *)
wenzelm@6932
   463
wenzelm@12146
   464
fun prep_result state ts raw_th =
wenzelm@5820
   465
  let
wenzelm@5820
   466
    val ctxt = context_of state;
wenzelm@5820
   467
    fun err msg = raise STATE (msg, state);
wenzelm@5820
   468
wenzelm@12146
   469
    val ngoals = Thm.nprems_of raw_th;
wenzelm@5820
   470
    val _ =
wenzelm@5820
   471
      if ngoals = 0 then ()
wenzelm@12085
   472
      else (err (Pretty.string_of (Pretty.chunks (pretty_goals_local ctxt "" (true, true)
wenzelm@12146
   473
            (! Display.goals_limit) raw_th @
wenzelm@12085
   474
          [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")]))));
wenzelm@5820
   475
wenzelm@12146
   476
    val {hyps, sign, ...} = Thm.rep_thm raw_th;
wenzelm@5820
   477
    val tsig = Sign.tsig_of sign;
wenzelm@12055
   478
    val casms = flat (map #1 (ProofContext.assumptions_of (context_of state)));
wenzelm@11816
   479
    val bad_hyps = Library.gen_rems Term.aconv (hyps, map Thm.term_of casms);
wenzelm@12146
   480
wenzelm@12146
   481
    val th = raw_th RS Drule.rev_triv_goal;
wenzelm@12146
   482
    val ths = Drule.conj_elim_precise (length ts) th
wenzelm@12146
   483
      handle THM _ => err "Main goal structure corrupted";
wenzelm@12146
   484
    val props = map (#prop o Thm.rep_thm) ths;
wenzelm@5820
   485
  in
wenzelm@12146
   486
    conditional (not (null bad_hyps)) (fn () => err ("Additional hypotheses:\n" ^
wenzelm@12146
   487
        cat_lines (map (ProofContext.string_of_term ctxt) bad_hyps)));
wenzelm@12146
   488
    conditional (exists (not o Pattern.matches tsig) (ts ~~ props)) (fn () =>
wenzelm@12146
   489
      err ("Proved a different theorem: " ^ Pretty.string_of (ProofContext.pretty_thm ctxt th)));
wenzelm@12146
   490
    ths
wenzelm@5820
   491
  end;
wenzelm@5820
   492
wenzelm@5820
   493
wenzelm@5820
   494
wenzelm@5820
   495
(*** structured proof commands ***)
wenzelm@5820
   496
wenzelm@5820
   497
(** context **)
wenzelm@5820
   498
wenzelm@5820
   499
(* bind *)
wenzelm@5820
   500
wenzelm@5820
   501
fun gen_bind f x state =
wenzelm@5820
   502
  state
wenzelm@5820
   503
  |> assert_forward
wenzelm@5820
   504
  |> map_context (f x)
wenzelm@5820
   505
  |> reset_facts;
wenzelm@5820
   506
wenzelm@8617
   507
val match_bind = gen_bind (ProofContext.match_bind false);
wenzelm@8617
   508
val match_bind_i = gen_bind (ProofContext.match_bind_i false);
wenzelm@8617
   509
val let_bind = gen_bind (ProofContext.match_bind true);
wenzelm@8617
   510
val let_bind_i = gen_bind (ProofContext.match_bind_i true);
wenzelm@5820
   511
wenzelm@5820
   512
wenzelm@9196
   513
(* have_thmss etc. *)
wenzelm@5820
   514
wenzelm@9196
   515
fun have_thmss args state =
wenzelm@5820
   516
  state
wenzelm@5820
   517
  |> assert_forward
wenzelm@9196
   518
  |> map_context_result (ProofContext.have_thmss args)
wenzelm@9196
   519
  |> these_factss;
wenzelm@5820
   520
wenzelm@9196
   521
fun simple_have_thms name thms = have_thmss [((name, []), [(thms, [])])];
wenzelm@9196
   522
wenzelm@9196
   523
fun with_thmss args state =
wenzelm@9196
   524
  let val state' = state |> have_thmss args
wenzelm@9196
   525
  in state' |> simple_have_thms "" (the_facts state' @ the_facts state) end;
wenzelm@6876
   526
wenzelm@5820
   527
wenzelm@5820
   528
(* fix *)
wenzelm@5820
   529
wenzelm@5820
   530
fun gen_fix f xs state =
wenzelm@5820
   531
  state
wenzelm@5820
   532
  |> assert_forward
wenzelm@5820
   533
  |> map_context (f xs)
wenzelm@5820
   534
  |> reset_facts;
wenzelm@5820
   535
wenzelm@5820
   536
val fix = gen_fix ProofContext.fix;
wenzelm@5820
   537
val fix_i = gen_fix ProofContext.fix_i;
wenzelm@5820
   538
wenzelm@5820
   539
wenzelm@11891
   540
(* assume and presume *)
wenzelm@5820
   541
wenzelm@9469
   542
fun gen_assume f exp args state =
wenzelm@5820
   543
  state
wenzelm@5820
   544
  |> assert_forward
wenzelm@9469
   545
  |> map_context_result (f exp args)
wenzelm@11924
   546
  |> these_factss;
wenzelm@6932
   547
wenzelm@7271
   548
val assm = gen_assume ProofContext.assume;
wenzelm@7271
   549
val assm_i = gen_assume ProofContext.assume_i;
wenzelm@11917
   550
val assume = assm ProofContext.export_assume;
wenzelm@11917
   551
val assume_i = assm_i ProofContext.export_assume;
wenzelm@11917
   552
val presume = assm ProofContext.export_presume;
wenzelm@11917
   553
val presume_i = assm_i ProofContext.export_presume;
wenzelm@5820
   554
wenzelm@7271
   555
wenzelm@5820
   556
wenzelm@11891
   557
(** local definitions **)
wenzelm@11891
   558
wenzelm@11891
   559
fun gen_def fix prep_term prep_pats raw_name atts (x, (raw_rhs, raw_pats)) state =
wenzelm@11891
   560
  let
wenzelm@11891
   561
    val _ = assert_forward state;
wenzelm@11891
   562
    val ctxt = context_of state;
wenzelm@11891
   563
wenzelm@11891
   564
    (*rhs*)
wenzelm@11891
   565
    val name = if raw_name = "" then Thm.def_name x else raw_name;
wenzelm@11891
   566
    val rhs = prep_term ctxt raw_rhs;
wenzelm@11891
   567
    val T = Term.fastype_of rhs;
wenzelm@11891
   568
    val pats = prep_pats T (ProofContext.declare_term rhs ctxt) raw_pats;
wenzelm@11891
   569
wenzelm@11891
   570
    (*lhs*)
wenzelm@11891
   571
    val lhs = ProofContext.bind_skolem ctxt [x] (Free (x, T));
wenzelm@11891
   572
  in
wenzelm@11891
   573
    state
wenzelm@11891
   574
    |> fix [([x], None)]
wenzelm@11891
   575
    |> match_bind_i [(pats, rhs)]
wenzelm@11917
   576
    |> assm_i ProofContext.export_def [((name, atts), [(Logic.mk_equals (lhs, rhs), ([], []))])]
wenzelm@11891
   577
  end;
wenzelm@11891
   578
wenzelm@11891
   579
val def = gen_def fix ProofContext.read_term ProofContext.read_term_pats;
wenzelm@11891
   580
val def_i = gen_def fix_i ProofContext.cert_term ProofContext.cert_term_pats;
wenzelm@11891
   581
wenzelm@11891
   582
wenzelm@8374
   583
(* invoke_case *)
wenzelm@8374
   584
wenzelm@11793
   585
fun invoke_case (name, xs, atts) state =
wenzelm@9292
   586
  let
wenzelm@10830
   587
    val (state', (lets, asms)) =
wenzelm@11793
   588
      map_context_result (ProofContext.apply_case (get_case state name xs)) state;
wenzelm@9292
   589
  in
wenzelm@10830
   590
    state'
wenzelm@10809
   591
    |> add_binds_i lets
wenzelm@10830
   592
    |> assume_i [((name, atts), map (rpair ([], [])) asms)]
wenzelm@8374
   593
  end;
wenzelm@8374
   594
wenzelm@8374
   595
wenzelm@5820
   596
wenzelm@5820
   597
(** goals **)
wenzelm@5820
   598
wenzelm@5820
   599
(* forward chaining *)
wenzelm@5820
   600
wenzelm@5820
   601
fun chain state =
wenzelm@5820
   602
  state
wenzelm@5820
   603
  |> assert_forward
wenzelm@6848
   604
  |> assert_facts
wenzelm@5820
   605
  |> enter_forward_chain;
wenzelm@5820
   606
wenzelm@5820
   607
fun from_facts facts state =
wenzelm@5820
   608
  state
wenzelm@5820
   609
  |> put_facts (Some facts)
wenzelm@5820
   610
  |> chain;
wenzelm@5820
   611
wenzelm@5820
   612
wenzelm@5820
   613
(* setup goals *)
wenzelm@5820
   614
wenzelm@11549
   615
val rule_contextN = "rule_context";
wenzelm@8991
   616
wenzelm@12534
   617
fun setup_goal opt_block prepp autofix kind after_qed names raw_propp state =
wenzelm@5820
   618
  let
wenzelm@12146
   619
    val (state', (propss, gen_binds)) =
wenzelm@5936
   620
      state
wenzelm@5936
   621
      |> assert_forward_or_chain
wenzelm@5936
   622
      |> enter_forward
wenzelm@8617
   623
      |> opt_block
wenzelm@12534
   624
      |> map_context_result (fn ctxt => prepp (ctxt, raw_propp));
wenzelm@12146
   625
wenzelm@12146
   626
    val props = flat propss;
wenzelm@12146
   627
    val cprop = Thm.cterm_of (sign_of state') (foldr1 Logic.mk_conjunction props);
wenzelm@7556
   628
    val goal = Drule.mk_triv_goal cprop;
wenzelm@10553
   629
wenzelm@12146
   630
    val tvars = foldr Term.add_term_tvars (props, []);
wenzelm@12146
   631
    val vars = foldr Term.add_term_vars (props, []);
wenzelm@5820
   632
  in
wenzelm@10553
   633
    if null tvars then ()
wenzelm@10553
   634
    else raise STATE ("Goal statement contains illegal schematic type variable(s): " ^
wenzelm@10553
   635
      commas (map (Syntax.string_of_vname o #1) tvars), state);
wenzelm@10553
   636
    if null vars then ()
wenzelm@10553
   637
    else warning ("Goal statement contains unbound schematic variable(s): " ^
wenzelm@12055
   638
      commas (map (ProofContext.string_of_term (context_of state')) vars));
wenzelm@5936
   639
    state'
wenzelm@12146
   640
    |> map_context (autofix props)
wenzelm@12146
   641
    |> put_goal (Some (((kind, names, propss), ([], goal)), after_qed o map_context gen_binds))
wenzelm@12167
   642
    |> map_context (ProofContext.add_cases
wenzelm@12167
   643
     (if length props = 1 then RuleCases.make true goal [rule_contextN]
wenzelm@12167
   644
      else [(rule_contextN, RuleCases.empty)]))
wenzelm@12146
   645
    |> auto_bind_goal props
wenzelm@5820
   646
    |> (if is_chain state then use_facts else reset_facts)
wenzelm@5820
   647
    |> new_block
wenzelm@5820
   648
    |> enter_backward
wenzelm@5820
   649
  end;
wenzelm@5820
   650
wenzelm@5820
   651
(*global goals*)
wenzelm@12534
   652
fun global_goal prep kind a raw_locale elems args thy =
wenzelm@12503
   653
  let
wenzelm@12549
   654
    val init = init_state thy;
wenzelm@12534
   655
    val (opt_name, locale_ctxt, elems_ctxt, propp) =
wenzelm@12549
   656
      prep (apsome fst raw_locale) elems (map snd args) (context_of init);
wenzelm@12534
   657
    val locale = (case raw_locale of None => None | Some (_, atts) => Some (the opt_name, atts));
wenzelm@12503
   658
  in
wenzelm@12549
   659
    init
wenzelm@12549
   660
    |> open_block
wenzelm@12511
   661
    |> map_context (K locale_ctxt)
wenzelm@12065
   662
    |> open_block
wenzelm@12511
   663
    |> map_context (K elems_ctxt)
wenzelm@12534
   664
    |> setup_goal I ProofContext.bind_propp_schematic_i
wenzelm@12534
   665
      ProofContext.fix_frees (Theorem (kind, a, locale, map (snd o fst) args))
wenzelm@12534
   666
      Seq.single (map (fst o fst) args) propp
wenzelm@12065
   667
  end;
wenzelm@5820
   668
wenzelm@12534
   669
val multi_theorem = global_goal Locale.read_context_statement;
wenzelm@12534
   670
val multi_theorem_i = global_goal Locale.cert_context_statement;
wenzelm@12146
   671
wenzelm@12242
   672
fun theorem k locale elems name atts p =
wenzelm@12242
   673
  multi_theorem k (name, atts) locale elems [(("", []), [p])];
wenzelm@12242
   674
fun theorem_i k locale elems name atts p =
wenzelm@12242
   675
  multi_theorem_i k (name, atts) locale elems [(("", []), [p])];
wenzelm@5820
   676
wenzelm@5820
   677
wenzelm@5820
   678
(*local goals*)
wenzelm@12146
   679
fun local_goal' prepp kind (check: bool -> state -> state) f args int state =
wenzelm@7928
   680
  state
wenzelm@12146
   681
  |> setup_goal open_block prepp (K I) (kind (map (snd o fst) args))
wenzelm@12146
   682
    f (map (fst o fst) args) (map snd args)
wenzelm@10936
   683
  |> warn_extra_tfrees state
wenzelm@10936
   684
  |> check int;
wenzelm@5820
   685
wenzelm@12146
   686
fun local_goal prepp kind f args = local_goal' prepp kind (K I) f args false;
wenzelm@10936
   687
wenzelm@10936
   688
val show = local_goal' ProofContext.bind_propp Show;
wenzelm@10936
   689
val show_i = local_goal' ProofContext.bind_propp_i Show;
wenzelm@10936
   690
val have = local_goal ProofContext.bind_propp Have;
wenzelm@10380
   691
val have_i = local_goal ProofContext.bind_propp_i Have;
wenzelm@5820
   692
wenzelm@5820
   693
wenzelm@5820
   694
wenzelm@5820
   695
(** conclusions **)
wenzelm@5820
   696
wenzelm@5820
   697
(* current goal *)
wenzelm@5820
   698
wenzelm@7176
   699
fun current_goal (State (Node {context, goal = Some goal, ...}, _)) = (context, goal)
wenzelm@5820
   700
  | current_goal state = raise STATE ("No current goal!", state);
wenzelm@5820
   701
wenzelm@7176
   702
fun assert_current_goal true (state as State (Node {goal = None, ...}, _)) =
wenzelm@6404
   703
      raise STATE ("No goal in this block!", state)
wenzelm@7176
   704
  | assert_current_goal false (state as State (Node {goal = Some _, ...}, _)) =
wenzelm@6404
   705
      raise STATE ("Goal present in this block!", state)
wenzelm@6404
   706
  | assert_current_goal _ state = state;
wenzelm@5820
   707
wenzelm@12010
   708
fun assert_bottom b (state as State (_, nodes)) =
wenzelm@12010
   709
  let val bot = (length nodes <= 2) in
wenzelm@12010
   710
    if b andalso not bot then raise STATE ("Not at bottom of proof!", state)
wenzelm@12010
   711
    else if not b andalso bot then raise STATE ("Already at bottom of proof!", state)
wenzelm@12010
   712
    else state
wenzelm@12010
   713
  end;
wenzelm@5820
   714
wenzelm@6404
   715
val at_bottom = can (assert_bottom true o close_block);
wenzelm@6404
   716
wenzelm@6932
   717
fun end_proof bot state =
wenzelm@5820
   718
  state
wenzelm@5820
   719
  |> assert_forward
wenzelm@5820
   720
  |> close_block
wenzelm@5820
   721
  |> assert_bottom bot
wenzelm@7011
   722
  |> assert_current_goal true
wenzelm@7011
   723
  |> goal_facts (K []);
wenzelm@5820
   724
wenzelm@5820
   725
wenzelm@6404
   726
(* local_qed *)
wenzelm@5820
   727
wenzelm@6982
   728
fun finish_local (print_result, print_rule) state =
wenzelm@5820
   729
  let
wenzelm@12146
   730
    val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), after_qed)) = current_goal state;
wenzelm@8617
   731
    val outer_state = state |> close_block;
wenzelm@8617
   732
    val outer_ctxt = context_of outer_state;
wenzelm@8617
   733
wenzelm@12146
   734
    val ts = flat tss;
wenzelm@12146
   735
    val results = prep_result state ts raw_thm;
wenzelm@12146
   736
    val resultq =
wenzelm@12146
   737
      results |> map (ProofContext.export false goal_ctxt outer_ctxt)
wenzelm@12146
   738
      |> Seq.commute |> Seq.map (Library.unflat tss);
wenzelm@9469
   739
wenzelm@12146
   740
    val (attss, opt_solve) =
wenzelm@5820
   741
      (case kind of
wenzelm@12146
   742
        Show attss => (attss, export_goals goal_ctxt print_rule results)
wenzelm@12146
   743
      | Have attss => (attss, Seq.single)
wenzelm@6932
   744
      | _ => err_malformed "finish_local" state);
wenzelm@5820
   745
  in
wenzelm@12146
   746
    print_result goal_ctxt (kind_name (sign_of state) kind, names ~~ Library.unflat tss results);
wenzelm@8617
   747
    outer_state
wenzelm@12549
   748
    |> auto_bind_facts (ProofContext.generalize goal_ctxt outer_ctxt ts)
wenzelm@9469
   749
    |> (fn st => Seq.map (fn res =>
wenzelm@12146
   750
      have_thmss ((names ~~ attss) ~~ map (single o Thm.no_attributes) res) st) resultq)
wenzelm@9469
   751
    |> (Seq.flat o Seq.map opt_solve)
wenzelm@7176
   752
    |> (Seq.flat o Seq.map after_qed)
wenzelm@5820
   753
  end;
wenzelm@5820
   754
wenzelm@6982
   755
fun local_qed finalize print state =
wenzelm@6404
   756
  state
wenzelm@6932
   757
  |> end_proof false
wenzelm@6871
   758
  |> finalize
wenzelm@6982
   759
  |> (Seq.flat o Seq.map (finish_local print));
wenzelm@5820
   760
wenzelm@5820
   761
wenzelm@6404
   762
(* global_qed *)
wenzelm@5820
   763
wenzelm@12085
   764
fun locale_prefix None f thy = f thy
wenzelm@12096
   765
  | locale_prefix (Some (loc, _)) f thy =
wenzelm@12096
   766
      thy |> Theory.add_path (Sign.base_name loc) |> f |>> Theory.parent_path;
wenzelm@12085
   767
wenzelm@12146
   768
fun locale_add_thmss None _ = I
wenzelm@12146
   769
  | locale_add_thmss (Some (loc, atts)) ths = Locale.add_thmss loc (map (rpair atts) ths);
wenzelm@12065
   770
wenzelm@6950
   771
fun finish_global state =
wenzelm@5820
   772
  let
wenzelm@12065
   773
    fun export inner outer th =
wenzelm@12065
   774
      (case Seq.pull (ProofContext.export false inner outer th) of
wenzelm@12065
   775
        Some (th', _) => th' |> Drule.local_standard
wenzelm@12065
   776
      | None => raise STATE ("Internal failure of theorem export", state));
wenzelm@12010
   777
wenzelm@12146
   778
    val (goal_ctxt, (((kind, names, tss), (_, raw_thm)), _)) = current_goal state;
wenzelm@12065
   779
    val locale_ctxt = context_of (state |> close_block);
wenzelm@12065
   780
    val theory_ctxt = context_of (state |> close_block |> close_block);
wenzelm@5820
   781
wenzelm@12146
   782
    val ts = flat tss;
wenzelm@12146
   783
    val locale_results =
wenzelm@12146
   784
      prep_result state ts raw_thm |> map (export goal_ctxt locale_ctxt);
wenzelm@12223
   785
    val results = locale_results
wenzelm@12223
   786
      |> map (Drule.strip_shyps_warning o export locale_ctxt theory_ctxt);
wenzelm@12065
   787
wenzelm@12242
   788
    val (k, (cname, catts), locale, attss) =
wenzelm@12146
   789
      (case kind of Theorem x => x | _ => err_malformed "finish_global" state);
wenzelm@12242
   790
    val (thy1, res') =
wenzelm@12065
   791
      theory_of state
wenzelm@12146
   792
      |> locale_prefix locale (PureThy.have_thmss [Drule.kind k]
wenzelm@12146
   793
          ((names ~~ attss) ~~ map (single o Thm.no_attributes) (Library.unflat tss results)))
wenzelm@12146
   794
      |>> locale_add_thmss locale (names ~~ Library.unflat tss locale_results);
wenzelm@12242
   795
    val thy2 = thy1 |> PureThy.add_thmss [((cname, flat (map #2 res')), catts)] |> #1;
wenzelm@12244
   796
  in (thy2, ((k, cname), res')) end;
wenzelm@5820
   797
wenzelm@10553
   798
(*note: clients should inspect first result only, as backtracking may destroy theory*)
wenzelm@6950
   799
fun global_qed finalize state =
wenzelm@5820
   800
  state
wenzelm@6932
   801
  |> end_proof true
wenzelm@6871
   802
  |> finalize
wenzelm@12065
   803
  |> Seq.map finish_global;
wenzelm@5820
   804
wenzelm@5820
   805
wenzelm@6896
   806
wenzelm@6896
   807
(** blocks **)
wenzelm@6896
   808
wenzelm@6896
   809
(* begin_block *)
wenzelm@6896
   810
wenzelm@6896
   811
fun begin_block state =
wenzelm@6896
   812
  state
wenzelm@6896
   813
  |> assert_forward
wenzelm@6896
   814
  |> new_block
wenzelm@6896
   815
  |> open_block;
wenzelm@6896
   816
wenzelm@6896
   817
wenzelm@6896
   818
(* end_block *)
wenzelm@6896
   819
wenzelm@6896
   820
fun end_block state =
wenzelm@6896
   821
  state
wenzelm@6896
   822
  |> assert_forward
wenzelm@6896
   823
  |> close_block
wenzelm@6896
   824
  |> assert_current_goal false
wenzelm@6896
   825
  |> close_block
wenzelm@6932
   826
  |> transfer_facts state;
wenzelm@6896
   827
wenzelm@6896
   828
wenzelm@6896
   829
(* next_block *)
wenzelm@6896
   830
wenzelm@6896
   831
fun next_block state =
wenzelm@6896
   832
  state
wenzelm@6896
   833
  |> assert_forward
wenzelm@6896
   834
  |> close_block
wenzelm@8718
   835
  |> new_block
wenzelm@8718
   836
  |> reset_facts;
wenzelm@6896
   837
wenzelm@6896
   838
wenzelm@5820
   839
end;
wenzelm@8152
   840
wenzelm@8152
   841
structure BasicProof: BASIC_PROOF = Proof;
wenzelm@8152
   842
open BasicProof;